Minimization of norms and the spectral radius of a sum of nonnegative matrices under diagonal equivalence
type: Item
instance of: scholarly article
title: Minimization of norms and the spectral radius of a sum of nonnegative matrices under diagonal equivalence
zbMATH Open document ID: 0859.15012
DOI: 10.1016/0024-3795(95)00521-8
author: Daniel Hershkowitz
author: Wenchao Huang
author: M. Neumann
author: Hans Schneider
published in: Linear Algebra and its Applications
publication date: 1997-03-25T00:00:00Z
review text: The authors generalize in various directions a result of \textit{S. Friedland} and \textit{S. Karlin} [Duke Math. J. 42, 459-490 (1975; Zbl 0373.15008)] on a lower bound for the spectral radius of a matrix that is positively diagonally equivalent to a doubly stochastic matrix. First, they complete the original result by characterizing the equality cases for doubly stochastic matrices of general zero-pattern. Further, they discuss the sums of matrices that are diagonally equivalent to doubly stochastic matrices. After introducing a lower bound for submultiplicative norms of such matrices and characterizing those cases in which the lower bound is attained, these results are used to obtain a lower bound for the spectral radius of such sums and to characterize the equality case for the spectral radius. Finally, they introduce a lower bound for the submultiplicative norms of sums of nonnegative matrices in terms of norms of certain generalized doubly stochastic matrices, characterize those cases in which the lower bound is attained, and also obtain a lower bound for the spectral radius of such sums and characterize the corresponding equality case.
reviewed by: Yang Yingchen
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B51
zbMATH DE Number: 931898
zbMATH Keywords: Frobenius normal form
zbMATH Keywords: spectral radius
zbMATH Keywords: doubly stochastic matrix
zbMATH Keywords: lower bound
MaRDI profile type: Publication
full work available at URL: 0024-3795(95)00521-8
OpenAlex ID: W2111044742
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description: scientific article; zbMATH DE number 931898